GUIDELINES FOR SPACE DEBRIS AND METEOROID IMPACT RISK ASSESSMENT WITH DRAMA/MIDAS
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GUIDELINES FOR SPACE DEBRIS AND METEOROID IMPACT RISK ASSESSMENT
WITH DRAMA/MIDAS
X. Oikonomidou(1) , V. Braun(2) , and S. Lemmens(1)
(1)
European Space Agency, Space Debris Office, Robert-Bosch-Str. 5, 64293 Darmstadt, Germany, Email:
{xanthi.oikonomidou, stijn.lemmens}@esa.int
(2)
IMS Space Consultancy at European Space Agency, Space Debris Office, Robert-Bosch-Str. 5, 64293 Darmstadt,
Germany, Email: vitali.braun@esa.int
ABSTRACT 2019 [3]. The space debris mitigation requirements of
the latest ISO standards are adopted by the European Co-
operation for Space Standardization (ECSS) [4].
The space debris mitigation guidelines require the as-
sessment of the impact risk with space debris and mete- One aspect of the space debris mitigation guidelines in-
oroid objects. In order to assess the collision probability volves assessing the risk from a space debris or mete-
and the impact consequences, statistical flux models as oroid impact during the design phase of a space mission.
well as impact and damage analysis tools are employed. Risk assessment studies may additionally be performed
DRAMA/MIDAS (Debris Risk Assessment and Mitiga- during the operational phase of the mission, if required.
tion Analysis/MASTER-based Impact Flux and Damage Impact risk analyses can help identify the most vulner-
Assessment) is a comprehensive tool that can be used able components in the design of a spacecraft, and take
during early mission phases. This paper proposes two important decisions to minimise the risks of a collision
methodologies to address the impact risk with space de- with a space debris or meteoroid object. Such analy-
bris and meteoroid particles using the new release of ses are of particular importance when the non-trackable
DRAMA/MIDAS 3.1.0: a) Break-up risk assessment and population is considered: trackable objects (larger than
b) Probability of damage or failure due to collision. In approximately 10 cm in LEO and 50-100 cm in GEO)
support of the international standards and ESA’s space are too large for shielding measures, and the main pro-
debris mitigation process, practical guidelines and in- tective actions against them are collision avoidance ma-
structive examples using the latest software release are noeuvres, which are performed if the assessed collision
presented. risk is deemed too high [5]. For objects that cannot be
tracked, or for spacecraft with no manoeuvre capabili-
Keywords: DRAMA; MIDAS; Space debris mitigation ties, statistical flux models, and impact and damage anal-
guidelines; Impact risk assessment. ysis tools can be used to assess the impact risk with space
debris or meteoroids, and decide on design changes (e.g.
shielding) to minimize the probabilities of a break-up or
the damaging of the satellite such that successful post-
1. INTRODUCTION mission disposal can no longer be achieved.
This paper provides practical guidelines on how the space
As the space debris population continues to grow rapidly,
debris mitigation requirements and standards can be met
the likelihood of collisions is expected to increase like-
using the new release of DRAMA/MIDAS 3.1.0. Break-
wise. In response to this challenge, the Inter-Agency
up risk analyses, as well as damage/failure analyses to as-
Space Debris Coordination Committee (IADC) published
sess the likelihood of a successful post-mission disposal
its first edition of the Space Debris Mitigation Guidelines
are presented in detail.
in 2002, aiming at limiting the debris released during op-
erations, minimising the risk of explosive break-ups and
collisions, and removing defunct objects from populated
areas. Following the publication of the IADC guidelines,
the International Organization for Standardization (ISO) 2. THE DRAMA SOFTWARE SUITE
took up the task of transforming the guidelines and prac-
tices from the IADC, also recognised on UN level, into a
set of international space debris mitigation standards [1]. The DRAMA software suite consists of several indepen-
The first ISO standards were published in 2010, and since dent tools designed to provide an assessment of the com-
then ten more standards have been released, with the third pliance of a user-defined mission with various aspects of
edition of the latest ISO 24113 standards published in the space debris mitigation guidelines [2]:
Proc. 8th European Conference on Space Debris (virtual), Darmstadt, Germany, 20–23 April 2021, published by the ESA Space Debris Office
Ed. T. Flohrer, S. Lemmens & F. Schmitz, (http://conference.sdo.esoc.esa.int, May 2021)• The Assessment of Risk Event Statistics (ARES) tool ment and Mitigation Analysis (DRAMA) software suite
allows to assess the annual rates of close approaches is an impact and damage analysis tool that can support
between an operational spacecraft and tracked ob- risk and vulnerability assessments, in the frame of evalu-
jects in Earth orbits along with statistics on the re- ating and reducing a space mission’s risk from space de-
quired number of collision avoidance manoeuvres, bris or meteoroid impacts during early mission planning.
and associated ∆v and propellant mass. The tool combines the orbital, mission and spacecraft pa-
rameters provided by the user and the debris and mete-
• The MASTER-based Impact Flux and Damage As- oroid flux from MASTER to result in an impact flux or a
sessment Software (MIDAS) facilitates the evalua- damage analysis. It accounts for:
tion of debris and meteoroid impact rates during the
lifetime of a satellite based on input coming from
ESA’s MASTER model and, by applying single and • the mission duration,
multiple wall equations, the probability of penetra-
tion for a given wall design. • the orbital regimes crossed and resided in,
• The Orbital SpaceCraft Active Removal (OSCAR) • the geometrical spacecraft parameters,
tool allows for the computation of the orbital life-
time and the evaluation of different disposal options • debris and meteoroid sources and population clouds,
after the End-of-Life (EOL).
• The re-entry Survival And Risk Analysis (SARA) • the evolution of the space debris environment.
tool accesses which and how many components of
a spacecraft would survive re-entry and computes MIDAS may additionally be used for top-level impact
the combined on-ground casualty risk given a world risk assessments during later stages of design, but it is
population model and the impact footprint of all sur- not always the most suitable solution. For a less con-
viving fragments. servative assessment, and/or further analyses using cloud
• The Cross-section Of Complex Bodies (CROC) tool modelling, and/or component shielding aspects, higher fi-
computes the cross-section of a 3D-modelled satel- delity tools can be employed [7].
lite, either randomly tumbling or taking a fixed ori-
entation and/or rotation axis. MIDAS supports two types of analysis modes [8]:
DRAMA was first released in 2004 and was upgraded 1. the Impact Flux Analysis,
to DRAMA-2 in 2014. In 2019 another major upgrade
was released with DRAMA-3 [2]. The latest DRAMA 2. the Damage Analysis.
version 3.1.0 introduces among others, additional fea-
tures in the MIDAS tool focused on this paper. The
background population used by both ARES and MIDAS The Impact Flux Analysis mode of the MIDAS tool can
uses the input from ESA’s MASTER-8 model. Both be used to assess the flux of the impacting particles on
DRAMA and MASTER are available as a free down- the surface of a spacecraft or launch vehicle. For a se-
load from ESA’s Space Debris Portal https://sdup. lected time frame and particle size range, the probability
esoc.esa.int/drama/ [6]. of collision with respect to time, as well as the proba-
bility of collision with respect to the mass and size of
the impactor are computed. In the frame of this paper,
the analysis can be used to assess the break-up risk of a
spacecraft or launch vehicle.
The Damage Analysis mode of the MIDAS tool can be
used to assess the damage caused by the impacting par-
ticles on the surface of the spacecraft or launch vehicle.
In the frame of this paper, the analysis can be utilized to
compute the probability of damage or failure due to col-
lision. The user has the option to study surfaces of the
spacecraft individually, as defined in an Earth-fixed, Sun-
fixed or inertially fixed frame [5]. The Damage Analy-
Figure 1. The DRAMA software suite sis of MIDAS includes pre-defined ballistic limit equa-
tions (BLEs) which can be used to compute the critical
particle diameter necessary to produce a component fail-
ure via perforation. In the new version of MIDAS the
2.1. The MIDAS Tool
original and the recalibrated (Rudolph) Schäfer-Ryan-
Lambert (SRL) BLEs, as well as the carbon fibre rein-
The MASTER-based Impact Flux and Damage Assess- forced polymer (CFRP) BLEs are introduced. The user
ment Software (MIDAS) tool of the Debris Risk Assess- may also define additional ballistic limit equations.3. GUIDELINES FOR IMPACT RISK ASSESS- 8. Determination of the catastrophic impact probability
MENT Pcat over the life cycle phase(s) duration.
9. Comparison of Pcat against the requirement proba-
Among others, the space debris mitigation guidelines re- bility Pmax . For Pcat < Pmax the requirement is met
quire an early assessment of the break-up (i.e. complete and the analysis is considered complete. For Pcat
or partial destruction of an object that generates space > Pmax the requirement is not met and iteration of
debris [3]) risk of a spacecraft or launch vehicle orbital the analysis is required. Revision of the analysis as-
stage, as well as an early assessment of the risk that a sumptions and improvement of the spacecraft mod-
space debris or meteoroid impact will prevent the suc- elling is advised to be performed in order to mini-
cessful mission disposal [3]). In the frame of this pa- mize the probability of a catastrophic collision.
per, two methodologies for assessing the on-orbit break-
up risk and the risk of an unsuccessful disposal are de-
scribed. 3.1.1. Break-up threshold
3.1. Break-up Risk Assessment A commonly used threshold for the assessment of a catas-
trophic collision with an impactor is the energy-to-mass
ratio (EMR). The EMR is defined as [10, 11]:
The process for assessing and reducing a spacecraft or
launch vehicle orbital stage risk from a space debris or
2
meteoroid impact is addressed and extensively discussed 1 Mc · Vimp
in [7], [9] and [10]. Based on the developed strategies, EM R = · (1)
2 Mt
guidelines for assessing the risk of the destructive struc-
tural break-up due to a space debris or meteoroid im-
pact (catastrophic collision) with DRAMA/MIDAS are where
proposed. The assessment of the partial break-up of a
spacecraft requires more complex considerations and is Mc the mass of the projectile (impacting space de-
not part of this analysis. The proposed analysis steps are bris or meteoroid object) in kg,
presented below. Mt the mass of the target (spacecraft or launch ve-
hicle) in kg,
Definition of input parameters Vimp the impact velocity (relative velocity between
projectile and target) in m/s.
1. Definition of the life cycle phase(s) of the spacecraft A typically accepted value for the EMR threshold for
or launch vehicle stage [3]. All phases before the catastrophic collisions is 40 J/g [11]:
spacecraft/launch vehicle’s end-of-life (EOL) shall
be considered, unless indicated differently by the se-
lected break-up requirements. EM R ≥ EM Rcc = 40 J/g (2)
2. Definition of the phase(s) duration over the orbit.
The new version of DRAMA/MIDAS 3.1.0 supports the
3. Definition of the orbit state vector and its evolution computation of the number of catastrophic impacts based
according to the phase(s) under analysis. on the EMR criterion, using the impact velocity and pro-
4. Definition of the design parameters of the spacecraft jectile mass computed by MASTER. In the frame of
or launch vehicle stage. this assessment, a catastrophic impact corresponds to the
complete break-up of the studied object (e.g. spacecraft
or launch vehicle stage).
Thresholds and requirements
5. Definition of a threshold above which a space debris 3.1.2. Break-up probability threshold
or meteoroid particle would cause the break-up of
the spacecraft or launch vehicle stage.
A globally supported value to limit the break-up prob-
6. Expression of the break-up requirement in terms of ability caused by space debris or meteoroids as part of
a maximum allowed probability value Pmax (e.g. the mission design has not yet been defined. However,
10−3 or 10−4 for LEO orbits). international standards such as [3] do limit the break-
up probability caused by internal sources of energy dur-
ing normal operations to 10−3 , based on the argument
MIDAS simulations and analysis that targeting this probability of occurrence would lead
to an order of magnitude reduction in on-orbit rates ob-
7. Determination of the number of catastrophic im- served. These break-ups currently drive the generation
pacts over the life cycle phase(s) duration. of the space debris environment. Therefore, it is sensibleto not accept a break-up probability caused by the envi- For the computation of the at-risk area, the protec-
ronment higher than the probability of break-up due to tion/shielding by other spacecraft components, the
internal causes. exposure to space and the directionality of the flux
with respect to the component under analysis are
In addition, it can be shown that an annual and per object taken into account. Example guidelines for comput-
catastrophic collision probability, in LEO, above 10−4 ing the at-risk area are provided in [10].
correlates with a long-term growth of the space debris
population [12]. As such, one can argue that such risk
Thresholds and requirements
should be mitigated, at least during normal operations
and possibly extended to the end of the orbital lifetime 6. Identification of the ballistic limit i.e. the impact-
for a critical orbital region such as LEO. induced threshold of failure for each critical sur-
face via the application of a dedicated ballistic limit
equation.
3.1.3. Catastrophic impact probability
7. Expression of the survivability requirement in terms
of a minimum allowed value of impact-induced
From the number of catastrophic impacts, the probability Probability of No Failure PNFmin of the spacecraft.
of a catastrophic impact Pcat may additionally be com- For DRAMA/MIDAS, the Probability of No Failure
puted by expressing the probability of the number of (PNF) corresponds to the Probability of No Pene-
catastrophic impacts as the complement of the probability tration (PNP). It is suggested to derive the value for
of no impact using Poisson statistics: PNFmin as part of the overall system requirement
for successful disposal (e.g. 0.90 in [3]).
Pcat = 1 − e−N (3)
MIDAS simulations and analysis
where N is the total number of catastrophic impacts. 8. Determination of the expected number of impacts
likely to cause damage or failure, which can option-
ally be used as an additional metric for the vulnera-
3.2. Probability of Damage or Failure due to Colli- bility assessment of the spacecraft.
sion
9. Determination of the Probability of No Failure
(PNF) for each critical component.
The probability analysis for assessing the vulnerability of
the spacecraft or launch vehicle stage to an impact with 10. Combination of the PNF of all critical components
space debris or meteoroids is addressed and discussed in and determination of the PNFS/C (of the space-
[7], [9] and [10]. Vulnerability assessment methodolo- craft).
gies using higher fidelity analysis tools have also been
developed (e.g. [13, 14, 15]). The assessment of the 11. Comparison of the computed PNFS/C with the re-
probability of damage or failure due to collision using quired PNFmin . For PNFS/C > PNFmin the analy-
DRAMA/MIDAS includes the following steps: sis is considered complete. For PNFS/C < PNFmin
the requirement is not met and an iteration is re-
quired. Revision of the analysis assumptions and
Definition of input parameters improvement of the spacecraft modelling is advised
to be performed first. Other options include us-
1. Definition of the life cycle phase(s) of the spacecraft age of a higher fidelity tool, changes of the space-
or launch vehicle stage [3]. All phases before the craft design, (e.g. wall thickness, materials, shield
spacecraft/launch vehicle’s end-of-life (EOL) shall structure or location of the critical components), re-
be considered, unless indicated differently by the se- orientation of the spacecraft or its components to
lected survivability requirements. minimize the impacts from space debris or mete-
oroids or orbit design change if the mission allows.
2. Definition of the phase(s) duration over the orbit. Additional testing to calibrate new BLEs can also be
performed [7, 9].
3. Definition of the orbit state vector and its evolution
according to the phase(s) under analysis.
4. END-TO-END EXAMPLES WITH MIDAS
4. Definition of the architectural design of the space-
craft or launch vehicle stage.
After launching DRAMA, the user can create a
5. Identification of the critical components i.e. the workspace folder for his/her project. In this example, two
components which, when damaged by an impact, projects are created:
would prevent a critical function e.g. disposal. For
each component, the most critical surface and the 1. Break-up risk assessment,
at-risk area of the surface is additionally identified.
2. Probability of damage or failure due to collision.4.1. General Guidelines August 1st, 2020, while the disposal phase will end after
a 5-year period, on August 1st, 2025.
Once the project folder have been created, the user can
select the MIDAS tool from the toolbox bar.
In the Basic Settings tab, the start and the end date of the
mission to be analysed need to be defined. The respective
orbital elements or orbital states can then be added. The
user is required to define the spacecraft parameters and
specify a size interval for the impactors to be considered
by MASTER.
In the Sources tab, the debris and/or meteoroid sources
to be considered in the analysis can be selected. The Figure 2. Basic parameters settings
user may either select the condensed population of MAS-
TER, which considers the contribution from all available Following the definition of the phases’ duration, the orbit
space debris sources, or study separately the contribution of the satellite needs to be defined. The orbit parameters
of the different sources. Population clouds of individual are added as single averaged elements in the correspond-
fragmentation events can also be independently analysed. ing MIDAS tab. We consider a sun-synchronous, near-
The meteoroid sources are not part of the condensed circular orbit, with an orbital height of 700 km. Due to
population or the population clouds, and their contribu- the stochastic nature of the space debris environment, the
tion can be considered by selecting a suitable meteoroid right ascension of the ascending node does not play a role
model. for LEO orbits in the frequency of close encounters and
is set to 0 deg. The argument of perigee, which is only
In the Analysis Mode tab the user can select between the relevant in case of eccentric orbits, is also set to 0 deg
two modes of analyses: a) Impact Flux Analysis and b) [16].
Damage Analysis. The Impact Flux Analysis can be used
to compute the number of expected impacts during the
life cycle phase duration as well as the probability of col-
lision. The new version of DRAMA/MIDAS 3.1.0 also
outputs the number of catastrophic impacts with respect
to the impactors mass and diameter. For this analysis
mode the surface of the spacecraft or launch vehicle stage
can either be defined as a sphere or a as randomly tum-
bling plate. When the user selects to perform a Damage
Analysis then, in addition to the flux estimates the Impact
Flux Analysis offers, the damage caused by the impact-
ing particles on a specified surface can be assessed. In Figure 3. Orbital parameters settings
this analysis mode up to 10 surfaces can be individually
analysed. For each selected surface, the orientation, the The design parameters of the satellite can be defined in
area, a ballistic limit equation and the wall specifications the Spacecraft parameters fields. A satellite with a cross-
need to be defined. sectional area of 5 m2 (main satellite body) and a mass
of 2100 kg is considered. For the drag and reflectivity
In the Plot Options tab the data lines which will be dis- coefficients, the default values are used.
played in the plots can optionally be customized. By de-
fault, four data lines will be displayed. The first three
lines represent the total of all debris sources, the total of
all meteoroid sources and the total of all clouds respec-
tively, while the fourth line represents the overall total
results.
4.2. Break-up Risk Assessment Figure 4. Spacecraft parameters settings
The fifth step of the break-up risk assessment requires
For the first example, a fictitious satellite in the Low the definition of a threshold above which a space de-
Earth Orbit (LEO) is considered. Following the method- bris or meteoroid particle would cause the break-up of
ology for performing a break-up risk assessment with the satellite. For this example, the complete break-up of
DRAMA/MIDAS described in section 3.1, the life cy- the satellite is assessed (catastrophic collision). MIDAS
cle phase of the satellite is defined first. For the selected computes the number of catastrophic impacts using the
example, all life cycle phases until the satellite’s EOL are 40 J/g EMR criterion. MASTER is used as a background
considered. It is assumed that the mission phase began on model in order to compute the flux as a function of size,impact direction and impact velocity. Using the MAS-
TER size and impact velocity output, MIDAS computes
the number of impacts that exceed the EMR threshold and
are therefore accounted as catastrophic impacts.
The sixth step of the assessment requires the expression
of the break-up requirement in terms of a maximum al-
lowed probability value Pmax . Based on section 3.1.1 the Figure 7. Impact Flux Analysis mode
value 10−4 is chosen. The size interval taken into ac-
count for the example considers all space debris and me-
teoroid object objects within the range 10 µm – 100 m.
It is assumed that particles with size less than 10 µm will
only cause degradation of the spacecraft’s surface and are
therefore not included in the simulation.
Figure 8. Plot options
Figure 5. Impactor size interval definition
Following the definition of the impactors’ size interval, The Impact Flux Analysis mode outputs a total of nine
the sources to be included in the analysis are selected. plots. The first three plots depict the overall number of
By selecting the Condensed Debris Sources, all debris impacts with respect to time, the impactor diameter and
sources, as included in the condensed population files impactor mass respectively.
of MASTER, are considered. The meteoroid fluxes are
modelled using the Grün model with a Taylor velocity In this particular example, a total number of 58.518 ob-
distribution. jects in the size range 10 µm – 100 m is estimated to
impact the satellite during the studied life cycle phases
(Fig. 9). Out of this total number of impacts, 77% is ex-
pected to be space debris impacts, while 23% meteoroid
impacts.
Figure 9. Number of total impacts vs time
The next three output plots show the probability of colli-
sion with respect to time, impactor diameter and impactor
mass. For this example, the probability of collision is al-
ready at 100% in 2020. The cumulative Probability of
Figure 6. Space debris and meteoroid sources Collision graphs vs mass and diameter (i.e. Fig. 10) de-
pict the increase of the impact probability with decreasing
For the break-up risk assessment, the Impact Flux Analy- mass/size of the impactor.
sis of MIDAS is selected. The satellite surface is defined
as a sphere. The last three plots of the Impact Flux Analysis results,
first introduced in DRAMA/MIDAS 3.1.0, are the Num-
Since no clouds are taken into account for this MIDAS ber of Catastrophic Impacts vs time (Fig. 11), mass and
run, the respective line is removed from the Plot Options. diameter (Fig. 12). Objects that exceed the size of 8 cm4.3. Probability of Damage or Failure due to Colli-
sion
In this example, the critical components of the previously
described LEO satellite are studied in the frame of as-
sessing the probability of the successful disposal of the
satellite. The definition of the phases and their duration,
as well as the orbital and main spacecraft parameters re-
main the same with steps 1-4 of the break-up risk assess-
ment. However, knowledge of the geometrical character-
istics of the satellite and the location and configuration of
the critical components is additionally required.
A simple 3D model of the satellite can be constructed
Figure 10. Probability of collision vs diameter
using DRAMA/CROC. For the particular example three
critical components are considered: the propellant tank,
in diameter are most likely to result in the break-up of positioned internally at the bottom of the satellite struc-
the satellite, however, during the operational phase of the ture (Fig. 13, green line-filled area), and two identical
spacecraft, a catastrophic collision with a tracked object batteries positioned internally at the upper part of the
can be mitigated with collision avoidance. Due to the structure (Fig. 13, purple line-filled area). It is presumed
higher flux of smaller objects, the number of catastrophic that components such as the electronics box or the AOCS
impacts seems to be increasing with decreasing object system are located in the centre of the satellite, with suf-
size. ficient separation and protection from impacts.
Following the identification of the critical components,
their critical surface needs to be defined and their area
at-risk needs to be computed. The critical surface of
the propellant tank is considered to be the surface fac-
ing the flight direction, since it is expected to be subject
to higher space debris and meteoroid flux, and therefore
more likely to suffer an impact that could result in dam-
age or failure. Since the critical surface of the tank is
equally protected by the satellite walls, the at-risk area
of the critical surface of the tank is the total area facing
the flight direction. Considering a spherical tank with a
diameter of 0.5 m2 , the at-risk area of the tank is approx-
imately 0.196 m2 (surface area of a circle).
Figure 11. Number of catastrophic impacts vs time Similarly, the at-risk area of the batteries is computed.
We assume cuboid Li-ion batteries, placed close to the
satellite wall, with one of their surfaces facing the flight
direction. We consider their critical surface as the surface
facing the flight direction, with their at-risk being the area
of the critical surface. The critical area for a battery with
dimensions 130 x 60 x 270 mm (width x depth x height)
positioned vertically next to the wall would be a 0.035 m2
(width x height).
Step six of the assessment requires the identification of
the ballistic limit to be used for each critical surface.
In all cases, the criterion for damage or failure is pen-
etration/perforation. It is assumed that the tank and the
batteries are positioned behind the structure walls of the
satellite, with different spacing between the bumpers and
the component’s front wall or cover plate. A suitable
Figure 12. Number of catastrophic impacts vs diameter equation to study components behind structure walls is
the SRL (Schäfer-Ryan-Lambert) equation, named after
The number of catastrophic impacts at the end of the 5- its developers. The SRL equation is an extension of the
year period is computed to be 0.82729E-04. The proba- ESA triple-wall equation, and can be used to study inter-
bility of catastrophic impact can be derived using Eq. 1: nal spacecraft equipment. The first and the second plates
Pcat = 1 − e−N = 0.00008. For this example, Pcat < (outer and inner bumper) represent the structure wall of
Pmax holds and the requirement is met. the spacecraft while the third plate represents the frontFigure 13. CROC satellite model
wall or cover plate of the equipment under analysis [17].
Step seven of the assessment requires the expression of
the survivability requirement in terms of a minimum al-
lowed PNFmin for the spacecraft. The selection of an op-
timal value should originate from the project needs and
the objective of the vulnerability assessment. [3] requires
to guarantee the post-mission disposal with at least 0.90 Figure 14. Propellant tank parameters
reliability, and for the particular example PNFmin = 0.90.
In order to determine the expected number of impacts the inner bumper 0.05 cm (density of 2.7 g/cm3 ). The
likely to cause damage or failure, as well as the PNF for spacing between the bumpers is 2 cm. Both batteries are
the three critical components, the Damage Analysis mode considered to be placed right next to the inner bumper,
of MIDAS needs to be selected. We define three surfaces with no spacing between their cover plate and the bumper.
to be analysed, by switching on three respective surface The thickness of the front wall of the battery is considered
tabs and providing the component-specific parameters in to be 0.1 cm, with a yield stress of 73 ksi.
the dedicated fields. For all surfaces, an Earth-oriented
reference frame is considered and the at-risk area of the
critical surface of the components is added in the Surface
area field.
For the propellant tank, the thickness of both outer and
inner bumpers is assumed to be 0.5 cm, with a density of
2.7 g/cm3 (aluminium). The thickness of the front wall of
the propellant tank is assumed to be 0.4 cm. We consider
a spacing of 10 cm between the inner bumper and the
wall of the cover plate, and a spacing of 2 cm between
the inner and outer bumper. The yield stress of the tank’s
cover plate is 73 ksi (aluminium alloy 7075-T651).
Table 1. Critical component specification
Critical At-risk
Critical surface BLE
component area (m2 )
Propellant Surface facing the
0.196 SRL
tank flight direction
Li-ion Surface facing the
0.035 SRL
Battery 1 flight direction
Li-ion Surface facing the
0.035 SRL
Battery 2 flight direction
Figure 15. Li-ion batteries parameters
For the two Li-ion batteries, the thickness of the outer A Damage Analysis run typically requires more time than
bumper is assumed to be 0.5 cm while the thickness of an Impact Flux Analysis run. For this example, the analy-Figure 16. Number of Penetrations vs time for the pro- Figure 18. Failure flux vs diameter for the propellant tank
pellant tank
Figure 17. Number of Penetrations vs time for one of the Figure 19. Failure flux vs diameter for one of the two
two identical Li-ion batteries identical batteries
sis produces four tabs: the first tab contains the plots and (Fig. 18, Fig. 19) and the corresponding data files. The
data files of the Flux Analysis for the spacecraft, while Failure Flux refers to a 1 m2 surface and the period of
the other three tabs contain the damage plots and data a year and therefore needs to be scaled according to the
files for each modelled component’s surface. For every surface area and the time period of interest [18].
surface, a total of 21 plots are included. In addition to
the Number of Impacts, the Probability of Collision and
the Number of Catastrophic Impacts plots, the Damage N oP = F lux × Area × T ime (4)
Analysis produces Failure Flux, Number of Penetrations,
Probability of no Penetration and Probability of Penetra- From the resulting NoPs we can infer that even though the
tion plots. All graphs are provided as a function of time, number of penetrations is increasing the longer the mis-
mass and diameter, and are accompanied by their corre- sion is in orbit, no particle is expected to cause damage or
sponding data file. failure throughout the mission and disposal phase of the
spacecraft. It is worth mentioning that, in this example,
Step eight of the assessment requires the determination of space debris with diameter smaller than approximately 2
the number of impacts likely to cause damage or failure. mm does not contribute to the Failure Flux of the propel-
As the failure criterion has been defined to be penetration, lant tank, while space debris smaller than 0.32 mm does
representative output plots and data files are the Number not contribute to the Failure Flux of the two batteries.
of Penetrations, the Number of No Penetrations as well
as the Failure Flux plots. The number of impacts that are The next step of the analysis requires the computation
expected to cause failure at the end of the studied period of the PNF of the individual critical components. The
can be found in the data file of the Number of Penetra- PNF of the components corresponds to the Probability
tions (NoP) cumulative plots (Fig. 16, Fig. 17). For the of No Penetration (PNP) plots and data files. The prob-
studied surfaces, NoPtank = 0.00062, while NoPbattery1 ability values for the at-risk area of the critical surface
= NoPbattery2 = 0.00122. of the three critical components can be extracted from
the corresponding data files. At the end of the life cycle
The number of impacts that will cause damage or failure phases period, PNFtank = 0.99938, while PNFbattery1 =
can additionally be assessed from the Failure Flux plots PNFbattery1 = 0.99878.ification Guidelines [10] and its upcoming revision, and
by reflecting the ISO 24113:2019 Space Debris Mitiga-
tion Requirements [3].
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Figure 20. Probability of No Failure vs time for the pro-
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7. Inter-Agency Space Debris Coordination Committee
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The Probability of No Failure of the spacecraft PNFS/C sion 7.1
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ical components: PNFS/C = PNFtank · PNFbattery1 · Assessment and Mitigation Analysis (DRAMA), Soft-
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